Parameterizing the Eddy Length Scale
$$K=u_{rms}∗{\Gamma * \color{red}{L_{eddy}} \over (1 + b1 * |u_{mean} - c|^2 /u_{rms}^2 (z=0)} $$
The three length scales under consideration:
- Rossby Deformation Radius $\quad\quad L_r = {c_r \over |f|}$
- Rossby Equatorial Radius $ \quad\quad= L_{req} = {\sqrt{c_r \over 2\beta}}$
- Rhine's Scale $ \quad\quad L_{Rh} = {\sqrt{u_{rms} \over \beta}} \sim {\sigma_{vi} \over \beta}$
The Rossby Deformation Radius $L_r$ depends on the the Baroclinic wave speed $c_r$ and the Coriolis force $f$. The CESM value of the first Baroclinic wave speed is derived as per eq 2.2 in Chelton 1998.
First Baroclinic Wave Speed $c_r$ Chelton vs CESM
In [1]:
%pylab inline
%run steering_setup ;
basedir='/scratch/jet'
###nc = Dataset(basedir+'/steering/g.e11.GIAF.T62_gx1v6.steer.007.pop.h.nday1.yr.0249.nc')
nc = Dataset(basedir+'/steering/g.e11.GIAF.T62_gx1v6.steer.007.pop.h.nday1.0249-01.nc')
omega=7.2921e-5
deg2rad=pi/180
f=2*omega*sin(lat*deg2rad)
In [2]:
### get Variable from file c_rossby is in cm/s convert to m/s
c_rossby = nc.variables['C_ROSSBY'][0,:,:]
#Resample (aka re-project, re-grid) the NCEP data to target grid. First with nearest neighbour resampling...
c_rossby_nearest = pyresample.kd_tree.resample_nearest(orig_def, c_rossby, \
targ_def, radius_of_influence=500000, fill_value=None)
c_rossby_mps = c_rossby_nearest/100.
fig1=MapZoneContour(lon_targcyc,lat_targcyc,c_rossby_mps,figsize=(14,9),
title="CESM First Baroclinic Wave Speed (m/s)",
fmt='%.1f' )
c_r_chelton=Image(filename=basedir+'/steering/chelton_sfig1.jpg')
display(c_r_chelton)
First Baroclinic Rossby Radius Chelton vs CESM
CESM Rossby deformation radius = $L_{eddy}$
$L_r = {c_r \over |f|}$
$L_{req} = {\sqrt{c_r \over 2\beta}}$
$\require{cancel} \cancel {L_{Rh} = {\sqrt{u_{rms} \over \beta}} \sim {\sigma \over \beta}}$
$L_{eddy} = min (L_r, L_{req}, \cancel{L_{Rh}}).$
In [3]:
fcor = nc.variables['FCOR'][0,:,:]
fcor_nearest = pyresample.kd_tree.resample_nearest(orig_def, fcor, \
targ_def, radius_of_influence=500000, fill_value=None)
absf=np.abs(fcor_nearest)
l_rossby_calc=c_rossby_nearest/absf
btp = nc.variables['BTP'][0,:,:]
btp_nearest = pyresample.kd_tree.resample_nearest(orig_def, btp, \
targ_def, radius_of_influence=500000, fill_value=None)
l_rossbyeq_calc=np.sqrt(c_rossby_nearest/(2*btp_nearest))
l_eddy_calc=np.minimum(l_rossby_calc,l_rossbyeq_calc)
### convert regridded radius from cm to km
cm2km=1.e-5
l_eddy_calc_km=l_eddy_calc*cm2km
clevs=[10,20,30,40,50,60,80,100,150,230]
fig2=MapZoneContour(lon_targcyc,lat_targcyc,l_eddy_calc_km,figsize=(14,9),
levels=clevs,
title="CESM First Baroclinic Rossby Radius (km) $L_{eddy} \sim min(l_r,l_{req})$",
fmt='%.1i' )
l_r_chelton=Image(filename=basedir+'/steering/chelton_fig2.jpg')
display(l_r_chelton)
Parameterizing the Zonal Eddy Phase Speed $\color{red}{c}$
$K=u_{rms}∗{\Gamma * L_{eddy} \over (1 + b1 * |u_{mean} - \color{red}{c}|^2 /u_{rms}^2 (z=0)} $
$\cancel{c = - \beta * {L_r^2}}$ $L_r$ too high at equator
$c = - \beta * L_{eddy}^2$
In [4]:
#beta
clevs=arange(1.e-14,25.e-14,1e-14)
fig,ax,cbar =MapContourg(lon_targcyc,lat_targcyc,btp_nearest,
levels1=clevs,
# norm=norm,
addzonal=True,
figsize=(14,5),
title="Beta (1/cm*s)")
l_eddy_calc_sq=l_eddy_calc*l_eddy_calc
clevs=np.logspace(1,15,40)
norm=LogNorm()
fig,ax,cbar =MapContourg(lon_targcyc,lat_targcyc,l_eddy_calc_sq,
addzonal=True,
levels1=clevs,
norm=norm,
figsize=(14,5),
title="$L_{eddy}^2 (cm^2)$ log scale")
#cbar.ax.get_xaxis().get_major_formatter().labelOnlyBase = True
#cbar.ax.get_yaxis().set_major_formatter(plt.LogFormatter(10, labelOnlyBase=True))
#ax.yaxis.set_major_locator(ticker.MultipleLocator)
#ax.yaxis.set_major_formatter(LogFormatter())
#cbar.formatter.set_scientific(False)
#cbar.formatter.set_powerlimits((0, 0))
#cbar.update_ticks()
cbar.set_ticks(np.logspace(1,15,15))
c=btp_nearest*l_eddy_calc*l_eddy_calc # units=1/(cm s) * cm^2 = cm/s
clevs=arange(-10,20,1)
fig,ax,cbar = MapContourg(lon_targcyc,lat_targcyc,c,
addzonal=True,
levels1=clevs,
# norm=norm,
setover='darkred',
figsize=(14,5),
title="eddy phase speed c = beta*leddy**2 (cm/s) linear scale(NOTE I'm plotting positive c here - changed to negative after this plot")
cbar.set_ticks(np.linspace(-10,20,7))
c=-1.*c
Hughes Phase Speed (cm/s) from Tulloch Marshall Smith '09
In [5]:
hughes_c=Image(filename=basedir+'/steering/Hughes_phase_speed.png')
display(hughes_c)
Parameterizing the Zonal Velocity $\color{red}{u_{mean}}$
$K=u_{rms}∗{\Gamma * L_{eddy} \over (1 + b1 * |\color{red}{u_{mean}} - c|^2 /u_{rms}^2 (z=0)} $
In [6]:
################# PLOT (u-c)^2 convert m^2/s^2 #######################
umean=nc.variables['U_MEAN'][0,:,:]
umean10_nearest = pyresample.kd_tree.resample_nearest(orig_def, umean,
targ_def, radius_of_influence=500000, fill_value=None)
umean10_mps=umean10_nearest*1.e-2
clevs=np.linspace(-60,60,40)
fig,ax,cbar=MapContourg(lon_targcyc,lat_targcyc,umean10_nearest,
addzonal=True,
figsize=(14,5),
levels1=clevs,
# setover='darkred',
# setunder='darkblue',
title="U zonal velocity (cm/s)")
#fig.subplots_adjust(left=0.15, right=.9, bottom=0.1, top=0.9);
cbar.set_ticks(arange(-60,60,10))
pylab.xlim([-20.,20.])
# get 2D versions of the lat and lon variables add longitude start point here!
lon_ecco_orig, lat_ecco_orig = np.meshgrid(lon_ecco[:], lat_ecco[:])
orig_ecco_def = pyresample.geometry.GridDefinition(lons=lon_ecco_orig, lats=lat_ecco_orig)
ecco_u_nearest = pyresample.kd_tree.resample_nearest(orig_ecco_def, ecco_u, \
targ_def, radius_of_influence=500000, fill_value=None)
ecco_u_nearest_masked=np.ma.masked_where(ecco_u_nearest<-10, ecco_u_nearest, copy=True)
#print ecco_u_cyc_masked[:,0]
clevs=np.linspace(-60,60,40)
#ecco_u_nearest = pyresample.kd_tree.resample_nearest(orig_def, ecco_u, \
# targ_def, radius_of_influence=500000, fill_value=None)
fig,ax,cbar=MapContourg(lon_targcyc,lat_targcyc,ecco_u_nearest_masked*100,
addzonal=True,
figsize=(14,5),
levels1=clevs,
# extend='both',
title="ECCO U zonal velocity (cm/s)")
cbar.set_ticks(arange(-60,60,10))
pylab.xlim([-20.,20.])
Out[6]:
In [8]:
clevs=-np.logspace(3,-3,20)
norm=matplotlib.colors.SymLogNorm(linthresh=1e-4, vmin=-1000, vmax=-.001)
fig,ax,cbar=MapContourg(lon_targcyc,lat_targcyc,c,
addzonal=True,
levels1=clevs,
norm=norm,
figsize=(14,5),
title="eddy phase speed c = beta*leddy**2 (cm/s) log scale")
# Customize y tick lables
yticks=[-1000,-500,-200,-100,-50,-20,-10,-5,-2,-1,-.500,-.200,-.1,-.05,-.02,-.01,-.005,-.002,-.001]
cbar.set_ticks(yticks)
cbar.set_ticklabels(yticks)
#ax.ticklabel_format(axis='y', style='sci', scilimits=(-2,2))
#majorFormatter = ticker.FormatStrFormatter('%.3f')
#majorLocator = ticker.LogLocator(base=10.0, subs=[1.0], numdecs=6, numticks=15)
#ticker.MultipleLocator(20)
#cbar.ax.yaxis.set_major_locator(majorLocator)
#cbar.ax.yaxis.set_major_formatter(majorFormatter)
#ax.yaxis.get_major_formatter().set_powerlimits((0, 1))
pylab.xlim([-200.,0.])
uminusc=umean10_nearest-c #units cm/s
clevs=np.linspace(0,25,25)
fig,ax,cbar=MapContourg(lon_targcyc,lat_targcyc,uminusc,
addzonal=True,
# norm=norm,
levels1=clevs,
figsize=(14,5),
title="U-c (cm/s) (max = %i/min = %i) (c calculated using Leddy)"%(uminusc.max(),uminusc.min()))
yticks=linspace(0,25,6)
zonalticks=np.linspace(0,20,3)
cbar.set_ticks(yticks)
cbar.set_ticklabels(yticks)
pylab.xlim([0,25])
pylab.xticks(zonalticks)
Out[8]:
In [9]:
bates_uminusc=Image(filename=basedir+'/steering/bates2013_uminusc.png')
display(bates_uminusc)
In [10]:
uminusc_mps_sq=uminusc*uminusc*1.e-4 #units cm/s*cm/s*m/100cm*m/100cm
clevs=np.logspace(-4,1,40)
norm=LogNorm()
fig,ax,cbar=MapContourg(lon_targcyc,lat_targcyc,uminusc_mps_sq,
addzonal=True,
levels1=clevs,
figsize=(14,5),
norm=norm,
title=" ${(U-c)}^2 {(m^2/s^2)}$ max = %g/min = %g (log scale) "%(uminusc_mps_sq.max(),uminusc_mps_sq.min()))
#customize colorbar ticks
yticks=[1e-4,3e-4,1e-3,3e-3,1e-2,3e-2,1e-1,3e-1,1,3,10]
cbar.set_ticks(yticks)
#customize zonal ticks
pylab.xlim([0,.06])
pylab.xticks([0,.03,.06])
clevs=np.linspace(0,.06,25)
fig,ax,cbar=MapContourg(lon_targcyc,lat_targcyc,uminusc_mps_sq,
addzonal=True,
levels1=clevs,
figsize=(14,5),
title=" ${(U-c)}^2 {(m^2/s^2)}$ max = %g/min = %g "%(uminusc_mps_sq.max(),uminusc_mps_sq.min()))
#customize colorbar ticks
yticks=[0,.02,.04,.06]
cbar.set_ticks(yticks)
#customize zonal ticks
pylab.xlim([0,.06])
pylab.xticks([0,.03,.06])
Out[10]:
In [11]:
bates_uminuscsq=Image(filename=basedir+'/steering/Bates_u_minus_c_sq.jpg')
display(bates_uminuscsq)
Parameterizing the root-mean-square eddy velocity $\color{red}{u_{rms}}$ and the Eady Growth Rate $\color{red}{\sigma_{vi}}$
$K=\color{red}{u_{rms}}∗{\Gamma * L_{eddy} \over (1 + b1 * |u_{mean} - c|^2 /u_{rms}^2 (z=0)} $
$u_{rms} = alpha*\color{red}{\sigma_{vi}}*L_{eddy}$
The original derivation of $\sigma_{vi}$:
$\sigma_{vi} = {f \over \sqrt{R_i}}$
with $R_i$ the vertically integrated (over the 100 – 2000 m depth range) Richardson number.
An alternate derivation of $\sigma_{vi}$ is:
$ R_i = {N^2 \over { ( \frac {\partial u}{\partial z} )^2 + ( \frac {\partial v}{\partial z} )^2} }$
$ N^2 = {{-g \over \rho_0 }\frac {\partial \rho}{\partial z}} $
After hydrostatic and geostrophic approximations
$f \frac {\partial v}{\partial z} = {{-g \over \rho_0 }\frac {\partial \rho}{\partial x}}; \quad\quad f \frac {\partial u}{\partial z} = {{g \over \rho_0 }\frac {\partial \rho}{\partial y}} $
so
$\frac {\partial v}{\partial z} = {{-1\over f}{g \over \rho_0 }\frac {\partial \rho}{\partial x}}; \quad\quad \frac {\partial u}{\partial z} = {{1\over f}{g \over \rho_0 }\frac {\partial \rho}{\partial y}} $
$\therefore$
$ R_i = {f^2 N^2 \over \underbrace{{ {g^2 \over \rho_0^2 } ( \frac{\partial \rho}{\partial y})^2 + {g^2 \over \rho_0^2 } ( \frac{\partial \rho}{\partial z})^2} }_\text{m^4}}\quad\quad = \quad\quad {f^2N^2 \over m^4} $
$\sigma_{vi} = {f \over \sqrt{R_i}}\quad = \quad {f \over \sqrt{{f^2N^2 \over m^4}}}\quad = \quad {{\cancel f m^2} \over \cancel f N}$
$RX_1 = RX_{east} = \Delta\rho_x = \rho_{i+1,j} - \rho_{i,j}$
$RY_1 = RY_{north} = \Delta\rho_y = \rho_{i,j+1} - \rho_{i,j}$
$RZ_1 = RZ_{k+1} = \Delta\rho_z = \rho_{k} - \rho_{k+1}$
$\displaystyle{1 \over L_{R_i}} \displaystyle\int_{2000m}^{100m} \left\lbrace { {-g\over\rho_0}{\frac {\partial \rho} {\partial z}} \over { {g^2 \over \rho_0^2 } \left[( \frac{\partial \rho}{\partial y})^2 + ( \frac{\partial \rho}{\partial z})^2\right] } } \right\rbrace dz$
Note: missing $f^2$ which will be cancelled when forming $\sigma_{vi}$
$\quad\quad$ so $\cdots$ this is not $R_i$
Implementation notes
For Level K
Numerator : Top $= -grav * RZ_{SAVE}(\cdots k+1) * dzwr(k)$
Denominator :
$ \begin{align} work1 = p25 & * ( RX(..,i_{east},k)^2 \\ & + RX(..,i_{west},k)^2 \\ & + RX(..,i_{east},k+1)^2 \\ & + RX(..,i_{west},k+1)^2 ) / DXT(i,j)^2 \\ \end{align} $
$ \begin{align} work2 = p25 & * ( RY(..,j_{north},k)^2 \\ & + RY(..,j_{south},k)^2 \\ & + RY(..,j_{north},k+1)^2 \\ & + RY(..,j_{south},k+1)^2 \\ \end{align} $
$work3 = {\left( TOP \over (grav^2*(work1+work2))\right)}*dzw(k)$
Notes:
1)Need to be careful at top and bottom of ocean
2)Accurate dzw(k) for each (i,j) to form $L_{R_i}$
3) When constructing $sigma$ itself, use $RZ_{SAVE}$ with a minimum N value
4) use eps2
In [12]:
sigma_old = nc.variables['SIGMA_AVG'][0,:,:]
sigma_old_nearest = pyresample.kd_tree.resample_nearest(orig_def, sigma_old, \
targ_def, radius_of_influence=500000, fill_value=None)
sigma_avg1 = nc.variables['SIGMA_AVG1'][0,:,:]
sigma_avg1_nearest = pyresample.kd_tree.resample_nearest(orig_def, sigma_avg1, \
targ_def, radius_of_influence=500000, fill_value=None)
clevs=arange(.005,.05,.0025)
fig,ax,cbar=MapContourg(lon_targcyc,lat_targcyc,sigma_avg1_nearest*86400,
levels1=clevs,
figsize=(14,5),
setunder='darkblue',
setover='darkred',
title="New Eady inverse time scale calc using alt sigma $(days^{-1}) \sim {{m^2} \over N}$")
yticks=[.01,.02,.03,.04,.05]
cbar.set_ticks(yticks)
tulloch_eady=Image(filename=basedir+'/steering/tulloch_eady.png')
display(tulloch_eady)
In [13]:
################# PLOT u_rms with Leddy #######################
cm2m=.01
alpha=5.
u_rms_leddy = alpha*sigma_avg1_nearest*l_eddy_calc # units = 1*1/s*cm = cm/s
u_rms_leddy_mps=u_rms_leddy*cm2m
clevs=np.linspace(0,.4,40)
fig,ax,cbar=MapContourg(lon_targcyc,lat_targcyc,u_rms_leddy_mps,
addzonal=True,
levels1=clevs,
figsize=(14,5),
title="$u_{rms} ({m \over s}) \quad alpha * \sigma * l_{eddy}$ (alpha=%i,max = %i/min = %i) "%(alpha,u_rms_leddy_mps.max(),u_rms_leddy_mps.min()))
#customize colorbar ticks
yticks=[0,.1,.2,.3,.4]
cbar.set_ticks(yticks)
#customize zonal ticks
pylab.xlim([0,.2])
pylab.xticks([0,.1,.2])
Out[13]:
In [14]:
bates_urms=Image(filename=basedir+'/steering/bates2013-urms.png')
display(bates_urms)
In [15]:
################# PLOT u_rms^2 convert m^2/s^2 #######################
u_rms_leddy_mps_sq=u_rms_leddy_mps*u_rms_leddy_mps
clevs=np.linspace(0,.06,40)
norm=LogNorm()
fig,ax,cbar=MapContourg(lon_targcyc,lat_targcyc,u_rms_leddy_mps_sq,
addzonal=True,
levels1=clevs,
figsize=(14,5),
title="$u_{rms}^2 ({m^2 \over s^2})$ (alpha=%i,max = %g/min = %g) "%(alpha,u_rms_leddy_mps_sq.max(),u_rms_leddy_mps_sq.min()))
#customize colorbar ticks
yticks=[0,.02,.04,.06]
cbar.set_ticks(yticks)
#customize zonal ticks
pylab.xlim([0,.06])
pylab.xticks([0,.03,.06])
Out[15]:
In [16]:
urms_bates=Image(filename=basedir+'/steering/Bates_urms_sq.jpg')
display(urms_bates)
In [17]:
uminusc_sq_ovr_urms_sq = uminusc_mps_sq/u_rms_leddy_mps_sq #units cm/s / cm/s
uminusc_sq_ovr_urms_sq_masked=np.ma.masked_where(uminusc_sq_ovr_urms_sq >100., uminusc_sq_ovr_urms_sq, copy=True)
clevs=np.logspace(-3,4,21)
norm=LogNorm()
fig,ax,cbar=MapContourg(lon_targcyc,lat_targcyc,uminusc_sq_ovr_urms_sq_masked,
addzonal=True,
levels1=clevs,
norm=norm,
figsize=(14,5),
setover='darkred',
setunder='darkblue',
title="${(U-c)}^2 \over u_{rms}^2$ (masking values over 100)")
#customize colorbar ticks
yticks=np.logspace(-3,4,15)
cbar.set_ticks(yticks)
#customize zonal ticks
pylab.xlim([0,100])
pylab.xticks([0,50,100])
clevs=arange(0,5,.1)
fig,ax,cbar=MapContourg(lon_targcyc,lat_targcyc,uminusc_sq_ovr_urms_sq_masked,
addzonal=True,
levels1=clevs,
figsize=(14,4),
setover='darkred',
setunder='darkblue',
title="${(U-c)}^2 \over u_{rms}^2$ (masking values over 100)")
#customize colorbar ticks
yticks=[0,2,4]
cbar.set_ticks(yticks)
#customize zonal ticks
pylab.xlim([0,8])
pylab.xticks([0,4,8])
Out[17]:
In [18]:
bates_uminusc_sq_ovr_urms_sq =Image(filename=basedir+'/steering/Bates_suppress.jpg')
display(bates_uminusc_sq_ovr_urms_sq )
Parameterizing the Mixing term $\color{red}{L_{mix}}$
$\color{red}{L_{mix}} = \Gamma * L_{eddy} * Suppression$
$\Gamma = 0.35$
$Suppression= {1 \over (1 + b1 * |u_{mean} - c|^2 /u_{rms (z=0)}^2 )}$
$\color{red}{L_{mix}} = {\Gamma * L_{eddy} \over (1 + b1 * |u_{mean} - c|^2 /u_{rms}^2 (z=0)}$
In [19]:
gamma=.35
b1=4.0
supp=1./(1+b1*uminusc_sq_ovr_urms_sq)
supp1b1=1./(1+1*uminusc_sq_ovr_urms_sq)
cm2m=.01
l_eddy_calc_m=l_eddy_calc*cm2m
lmix=gamma*l_eddy_calc_m*supp
lmix1b1=gamma*l_eddy_calc_m*supp1b1
clevs=np.logspace(0,5,40)
norm=LogNorm()
fig,ax,cbar=MapContourg(lon_targcyc,lat_targcyc,lmix,
addzonal=True,
norm=norm,
levels1=clevs,
figsize=(14,5),
title="$L_{mix} = {\Gamma * L_{eddy} * Suppression} $")
pylab.xlim([0,10e3])
cbar.set_ticks([1,3,1e1,3e1,1e2,3e2,1e3,3e3,1e4,3e4,1e5])
clevs=np.linspace(0,1,30)
norm=matplotlib.colors.Normalize()
fig,ax,cbar=MapContourg(lon_targcyc,lat_targcyc,supp,
addzonal=True,
levels1=clevs,
figsize=(14,5),
title="Suppression factor ${1 \over (1 + b1 * |u_{mean} - c|^2 /u_{rms (z=0)}^2)}$")
#customize colorbar ticks
yticks=np.linspace(0, 1, 6)
cbar.set_ticks(yticks)
#customize zonal ticks
pylab.xlim([0,.8])
pylab.xticks([0,.25,.5,.75])
Out[19]:
In [20]:
bates_suppression =Image(filename=basedir+'/steering/bates2013_suppression.png')
display(bates_suppression )
Parameterizing Eddy diffusivity $\color{red}{K}$
$\color{red}{K}=u_{rms}∗L_{mix}$
In [21]:
kdiff=u_rms_leddy_mps*lmix
kdiff1b1=u_rms_leddy_mps*lmix1b1
clevs=np.logspace(0,4,40)
norm=LogNorm()
fig,ax,cbar=MapContourg(lon_targcyc,lat_targcyc,kdiff,
addzonal=True,
norm=norm,
levels1=clevs,
figsize=(14,5),
title="Eddy diffusivity $K$ (log scale)")
#customize colorbar ticks
yticks=np.logspace(0, 4,5)
cbar.set_ticks(yticks)
#customize zonal ticks
pylab.xlim([0,11e3])
pylab.xticks([0,5e3,10e3])
clevs=np.linspace(0,1.e4,40)
fig,ax,cbar=MapContourg(lon_targcyc,lat_targcyc,kdiff,
addzonal=True,
levels1=clevs,
figsize=(14,5),
title="Eddy diffusivity $K$ ")
#customize colorbar ticks
#cbar.set_ticks([1,3,1e1,3e1,1e2,3e2,1e3,3e3,1e4,])
yticks=np.linspace(0, 10000,6)
print yticks
cbar.set_ticks(yticks)
#customize zonal ticks
pylab.xlim([0,11e3])
pylab.xticks([0,5e3,10e3])
clevs=np.linspace(0,1.e4,40)
fig,ax,cbar=MapContourg(lon_targcyc,lat_targcyc,kdiff1b1,
addzonal=True,
levels1=clevs,
figsize=(14,5),
title="Eddy diffusivity $K$ With a suppression scaling factor $b1$ of 1 instead of 4")
#customize colorbar ticks
#cbar.set_ticks([1,3,1e1,3e1,1e2,3e2,1e3,3e3,1e4,])
yticks=np.linspace(0, 10000,6)
print yticks
cbar.set_ticks(yticks)
#customize zonal ticks
pylab.xlim([0,11e3])
pylab.xticks([0,5e3,10e3])
Out[21]:
In [22]:
bates_k =Image(filename=basedir+'/steering/bates2013_K.png')
display(bates_k )
Steering Level status
1. L_eddy values ok
2. Rossby wave speed ok
3. Eady inverse timescale ok
a. Use alternate calculation otherwise has problems at equator and
b.Richardson averages are too high causing sigma to drop too low
4. Zonal Eddy Phase Speed (c)
a. Too high 10S:10N
b. Missing westward velocities in ACC which appear
in Hughes Data used in this parameterization
5. (U-c) Because of problem with c this term is also too high 10S:10N.
6. U_rms (alpha*sigma*l_eddy) OK
a. Using alpha of 5
7. Zonal mean velocity looks ok compared to ECCO annual average
8. Suppression OK
9. K is low by a factor of 5
Todo
1. Need to work on Zonal phase speed c
2. Plot vertical distribution of K
In [23]:
urms_bates2=Image(filename=basedir+'/steering/Bates-Tulloch-etal-2014-002.jpg')
urms_bates3=Image(filename=basedir+'/steering/Bates-Tulloch-etal-2014-003.jpg')
urms_bates4=Image(filename=basedir+'/steering/Bates-Tulloch-etal-2014-004.jpg')
urms_bates5=Image(filename=basedir+'/steering/Bates-Tulloch-etal-2014-005.jpg')
urms_bates6=Image(filename=basedir+'/steering/Bates-Tulloch-etal-2014-006.jpg')
urms_bates7=Image(filename=basedir+'/steering/Bates-Tulloch-etal-2014-007.jpg')
urms_bates8=Image(filename=basedir+'/steering/Bates-Tulloch-etal-2014-008.jpg')
urms_bates9=Image(filename=basedir+'/steering/Bates-Tulloch-etal-2014-009.jpg')
urms_bates10=Image(filename=basedir+'/steering/Bates-Tulloch-etal-2014-010.jpg')
urms_bates11=Image(filename=basedir+'/steering/Bates-Tulloch-etal-2014-011.jpg')
display(urms_bates3,urms_bates4,urms_bates5,urms_bates6,urms_bates7,urms_bates8,urms_bates9,urms_bates10,urms_bates11)
CESM $U_{mean} = U_{resolved}$ integraged over {10,50,100,200,500} meters
In [24]:
umean_cesm=Image(filename=basedir+'/steering/umean.jpg')
display(umean_cesm)
In [25]:
bates_len_vel=Image(filename=basedir+'/steering/bates_len_vel.jpg')
display(bates_len_vel)
